Lectures by James L. Pazun 6 Circular Motion and Gravitation

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Goals for Chapter 6 To understand the dynamics of circular motion. To study the unique application of circular motion as it applies to Newton’s Law of Gravitation. To examine the idea of weight and relate it to mass and Newton’s Law of Gravitation. To study the motion of objects in orbit as a special application of Newton’s Law of Gravitation.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley In section 3.4 We studied the kinematics of circular motion. – Centripetal Acceleration – Changing velocity vector – Uniform Circular Motion We acquire new terminology. – Radian – Period – Frequency

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Velocity changing from the influence of a c - Figure 6.1 A review of the relationship between v and a c. The velocity changes direction, not magnitude.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Details of uniform circular motion - Example 6.2 Notice how v becomes linear when F c vanishes.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Model airplane on a string - Example 6.1 See the worked example on page 164.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley A tetherball problem – Example 6.2 and Figure 6.5 Refer to the worked example on page 165.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Rounding a flat curve – Example 6.3 and Figure 6.6 The centripetal force coming only from tire friction. Refer to the worked example on page 166.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Rounding a banked curve – Example 6.4 and Figure 6.7 The centripetal force comes from friction and a component of force from the car’s mass Refer to the worked problem, Example 6.4.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Dynamics of a Ferris Wheel – Example 6.5 and Figure 6.8 Refer to the worked example on page 168.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Walking approximated with U.C.M. – Figure 6.10 Each stride is taken as one in a series of arcs

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Newton’s Law of Gravitation – Figure 6.12 Always attractive. Directly proportional to the masses involved. Inversely proportional to the square of the separation between the masses. Masses must be large to bring F g to a size even close to humanly perceptible forces.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley A diagram of gravitational force

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley The gravitational force calculated – Example 6.6 Use Newton’s Law of Universal Gravitation with the specific masses and separation. Refer to the worked example on page 172.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley This may be done in a lab. – Figure 6.13 The slight attraction of the masses causes a nearly imperceptible rotation of the string supporting the masses connected to the mirror. Use of the laser allows a point many meters away to move through measurable distances as the angle allows the initial and final positions to diverge.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Even within the earth itself, gravity varies. – Figure 6.16 Distances from the center of rotation and different densities allow for interesting increase in F g. See the worked example on pages

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Gravitational force falls off quickly. – Figure 6.15 If either m 1 or m 2 are small, the force decreases quickly enough for humans to notice.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Gravitation applies elsewhere. – Figure 6.17 See the worked example on pages

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley What happens when velocity rises? – Figure 6.19 Eventually, F g balances and you have orbit. When v is large enough, you achieve escape velocity.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Calculations of satellite motion – Figure 6.21 Work on an example of a relay designed to stay in orbit permanently. See the solved example on page 177.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley If an object is massive, even photons cannot escape. A “black hole” is a collapsed sun of immense density such that a tiny radius contains all the former mass of a star The radius to prevent light from escaping is termed the “Schwarzschild Radius” The edge of this radius has even entered pop culture in films. This radius for light is called the “event horizon”